Multiscale dynamics of charging and plating in graphite electrodes coupling operando microscopy and phase-field modelling

The phase separation dynamics in graphitic anodes significantly affects lithium plating propensity, which is the major degradation mechanism that impairs the safety and fast charge capabilities of automotive lithium-ion batteries. In this study, we present comprehensive investigation employing operando high-resolution optical microscopy combined with non-equilibrium thermodynamics implemented in a multi-dimensional (1D+1D to 3D) phase-field modeling framework to reveal the rate-dependent spatial dynamics of phase separation and plating in graphite electrodes. Here we visualize and provide mechanistic understanding of the multistage phase separation, plating, inter/intra-particle lithium exchange and plated lithium back-intercalation phenomena. A strong dependence of intra-particle lithiation heterogeneity on the particle size, shape, orientation, surface condition and C-rate at the particle level is observed, which leads to early onset of plating spatially resolved by a 3D image-based phase-field model. Moreover, we highlight the distinct relaxation processes at different state-of-charges (SOCs), wherein thermodynamically unstable graphite particles undergo a drastic intra-particle lithium redistribution and inter-particle lithium exchange at intermediate SOCs, whereas the electrode equilibrates much slower at low and high SOCs. These physics-based insights into the distinct SOC-dependent relaxation efficiency provide new perspective towards developing advanced fast charge protocols to suppress plating and shorten the constant voltage regime.

the electrode-separator interface)? This was not clear, and again, might be more clearly shown when adding the cell geometry information to the main text. 6) In the paragraph below figure 1, "nominal current density" is used for the first time. What is meant by this, and how does it relate to "effective C-rate" described above? 7) Overall, the reviewer found the optical microscopy section the most difficult to follow-in the paper. It was not clear how some of these terms were defined (C-rate, current density, etc." relative to the areal capacity fo the porous electrode relative to the current collector, vs. the direction of lithiation. It should be emphasized to the reader if this visualization is actually in the in-plane (lateral direction) of a "typical" electrode, and that the corresponding direction of SoC gradients observed is perpendicular to what is normally considered the "thickness" direction, which was unclear. That would help to clarify several of the points above. 8) All of the experiments in this paper appear to be 2-electrode measurements with a Li metal counter electrode and no reference electrode. Therefore, in the experimental voltage curves, although the graphite potential is plotted as "vs Li/Li+", the effects of overpotentials at the Li metal counter electrode (which is not at 0V during non-zero currents) and IR drop will impact the measured potential. It was not clear, therefore, how it could be determined that 20 mV is the energy barrier for nucleation. This was also confusing, because it was not clear if the authors were stating that the electric potential of the composite graphite anode (composed of many particles at different SOC) is the nucleation barrier, or if this barrier applies to the electrochemical potential of individual graphite particles, which are at different SOC. Please clarify how this single number is used in this definition, and how it relates to inter-particle SoC heterogeneity. 9) The discussion of the individual particle geometries, orientations, size effects etc. was great, and a true highlight of the paper. One thing that was not clear is the term "Li flow direction". What is meant by that? Are the authors referring to the vector pointing normal to the electrode/separator interface? Li is clearly "flowing" in 3-dimensions within this 3-d electrode geometry, so this terminology was not clear. How does this "flow direction" relate to the electric field direction in the electrolyte phase surrounding these individual particles? It seems that the electrolyte potential gradients will also lead to a 3-D distribution of the electric field in the vicinity of the individual particles, so it was not clear what the "flow direction" indicates. 10) The authors state that "intra-particle SOC heterogeneity cannot be captured by macroscopic modelling techniques and yet is the major cause of the early onset of lithium plating". What is meant by "the major cause"? Inter particle heterogeneity (including SoC gradients throughout the electrode thickness) lead to local current focusing, which accelerates intra-particle heterogeneity. So it seems that both intra-and inter-particle SoC heterogeneity are coupled in a composite electrode, and we can not state that one is the "major cause" vs. the other. 11) The 3-D microstructure characterization section provides details that do not seem to directly relate to the rest of the story of the paper. For example, it was not clear how the details in Fig. 3dj directly relate to the discussion? Perhaps the most relevant point is the significant differences in tortuosity factor in the vertical vs. horizontal directions. It is worth mentioning that the optical cell geometry will thus experience greater electrolyte transport limitations than the coin cell, if the direction of "thickness" is in the horizontal direction. 12) In discussing the OCV profile, the authors state that "The inflection of the OCV curve is known to be an indication of lithium plating42, 43. The curve is divided into two plateaus, the first of which corresponds to the stripping process and the dissolved lithium back-intercalating in a deeper area of the electrode to maintain neutrality, thus slowing down the rise of the OCV curve and delaying the equilibration.". This plateauing behavior during OCV, and the deflections associated with stripping of plated Li, re-intercalation, and the delayed onset of equilibration are described in detail in Ref. 37, which would be good to cite here. In general, Ref. 37 provides a few relevant observations that further strengthen the discussion in the current paper, including a direct observation that Li plating nucleates on individual particles that lithiate fastest (the particles that experience the highest local SOC and turn gold first are the same particles where Li plating nucleates"), as well as the fact that the OCV peaks shift to longer times when the C-rate and thickness increase (discussion of Fig. 4). 13) Fig. 4a was difficult to interpret, as the panel is quite small with several labels and multiple voltage curves. It would be helpful to increase the width of this panel in the figure, to improve readability. 14) It was a bit surprising to see significant Li plating at a 1C rate for relatively "modest" electrode loadings of 1-2 mAh/cm2. Do typical commercial Li ion batteries experience plating at 1C for these loadings? It would be useful to benchmark these observations of plating at 1-2C rates for 1-2 mAh/cm2 loadings with other reports in the literature; for example K. G. Gallagher et al., J. Electrochem. Soc. 2016, 163 (2), A138-A149. 15) No SOC "color bar" was provided in Fig 5a. Is it the same color scale as Fig. 5b? In general, the use of a color scale to represent SoC and current density in the same figure (Fig. 5) makes the figure a bit confusing to follow, especially with two different color scale bars for current density in panels c-e. 16) In the later parts of the paper, a CC-CV charging protocol with a cutoff voltage in graphite potential was introduced, but this was not clearly explained: was this the first time that a CC-CV protocol was used? And was it only used on some experiments in the paper? 17) In the summary of the charge-protocol section, it is stated that the section provides proof that a relaxation step can allow for "complete stripping of any heterogeneous early plating". It was unclear how this was proven? Given the low Coulombic efficiency of Li plating and stripping in carbonate electrolytes, it seems unlikely that any rest protocol would allow for "complete stripping", implying that early plating can be completely reversed. If the authors observe this, please explain how this is definitively proven.

Reviewer #2 (Remarks to the Author):
This work investigates the phase-separation and plating phenomenon in graphite-based anode using In operando optical microscope and multiscale phase-field model. The experiments reveal the lithiation and plating/stripping behavior, along with their associated voltage profile for different currents. The study proposes mechanisms for how Li plating occurs at high rates, which are confirmed by multiscale phase-field simulations that aim to correlate microscopic investigations to macroscopic observations. Authors emphasize the importance of relaxation in enabling an efficient fast charging process, and the optimal relaxing times for each rate are suggested. Overall, the manuscript is well written and high quality. However, there are some areas to improve: 1. 3D image-based phase-field model has been used to demonstrate that the early onset of plating is related to a strong dependence of intra-particle lithiation heterogeneity on the particle size, shape, orientation, surface condition and C-rate. Phase-field model relies on the energy functional and thermodynamic/kinetic coefficients. The complexity of the problem should have phase-field model built with some assumptions which however are not clearly provided. In fact, some experimental evidence should be included to justify these assumptions. In other words, it would help if some experimental characterizations on the microscopic plating initiation could be included. 2. Since authors performed deep microscopic investigation, could authors suggest the optimal size and distribution of graphite particles for fast charging applications? 3. The details of how the simulations are performed, including initial/boundary conditions for both the 1D and 3D phase-field models, are not clear. 4. In all figures, the authors should clearly indicate which curve or plot corresponds to experimental observations and which is predicted.

Reviewer #1 (Remarks to the Author):
This ar cle describes a mul -modal study of graphite anodes during charging and OCV rest periods. Gradients in SOC are observed and modeled at both the intra-par cle and inter-par cle levels. The influence of par cle size, shape, and orienta on, are discussed on local heterogeneity. Finally, the inser on of 3-min OCV rest periods are studied to allow for SoC relaxa on to delay Li pla ng.
Overall, this is an interes ng ar cle that will provide value to the fast-charging community. In par cular, the discussion of intra-par cle SOC gradients is under-discussed in the literature, and provides high impact. Observa ons of individual par cle shape and orienta on effects are interes ng and relevant to understand heterogeneity at small length scales. However, there were several confusing and unclear aspects to the discussion, which made the paper hard to follow at mes. The reviewer is suppor ve of publica on in Nature Communica ons, a er the following points are addressed: 1) The defini on of C-rate and current density during the operando op cal microscopy experiments were unclear and difficult to follow at several points in the discussion. First: what area was used to define current density in these experiments? As discussed throughout, the local current density actually varies spa ally throughout the electrode surface in thick electrodes. Typically, an areal current density is defined, when the area of the working and counter electrodes are the same, and are placed in a parallel electrode geometry. However, in this op cal experiment, it was not clear what direc on the electric field is poin ng (is it normal to the electrode thickness, or in the lateral direc on?) Figure S1 was difficult to interpret, with respect to the loca on of the working and counter electrodes, and the perspec ve from which the op cal imaging is taken. A more detailed schema c with labels and arrows showing these direc ons would be helpful.
Based on these difficul es in visualizing the setup, the discussion of "thickness" and "interface" were also confusing, as discussed in a later comment. A significant part of this challenge is that the actual op cal cell geometry, with the working, counter electrodes, separator etc. are in the SI. The reviewer feels that this informa on should be moved to the main text, and the defini on of current density and Crate need to be more clearly explained for the op cal cell. For example, the authors state "Here a current density of 2 mA cm-2 corresponds to the current density of 1C in the coin cell experiment of this study, but the effec ve C-rate of the former is much lower due to the large geometry of the electrode". What is meant by "effec ve C-rate"? Please define current density and C-rate more mathema cally for the op cal cell, with visualiza ons of the electric field and electrode orienta ons in the main text.
The authors would like to express their gra tude to the Reviewer for bringing to their a en on the presence of confusing content. The current density was defined as the ra o of the total current and the 4 lateral surface areas of the electrode, as there is no intercala on reac on from the top and bo om planes. The direc on of the electric field is poin ng in the lateral direc on. In response to the Reviewer's request, the authors have made extensive revisions to the manuscript. The first paragraph of the Results sec on now contains more detailed explana ons regarding the defini on of the current density, the geometry of the cell, and the direc on of Li+ flow (electric field) in both the lateral and thickness direc ons. These addi ons have been highlighted for ease of reference. Furthermore, a new Figure 1 has been included to provide graphical illustra ons of these concepts, replacing the original Figure S1, which has been removed from the Supplementary Informa on.
With regard to the term "effec ve C-rate," the authors intended to convey the difficulty in accurately es ma ng a C-rate in the op cal cell geometry. This is due to the large (lateral) thickness of the graphite strip, which results in under-lithia on in the center region caused by the electrolyte concentra on gradient. Consequently, the "effec ve" capacity is actually lower than the nominal capacity. Moreover, despite having an iden cal areal current density, the C-rate in the op cal experiment is significantly smaller compared to the conven onal coin cell setup, primarily due to the substan ally smaller lateral reac ng surface. As a result, the C-rate in the op cal experiment cannot be directly compared to that of the coin cell setup. For these reasons, the authors avoided using "C-rate" to interpret the result of the operando op cal experiment, instead, the lithia on me in hours is used. To mi gate any confusion stemming from this, the authors have made the decision to remove the term "effec ve C-rate" from the manuscript. It is important to note that this term appeared only once in the manuscript and its removal has minimal impact on the overall understanding of the content.
2) Following on point 1, how is C-rate defined in the op cal experiments? Typically, the C-rate is based on the charge current needed to fully charge the electrode, based on the areal capacity (e.g. 2 mAh/cm2) and corresponding current density. However, it was not clear what the areal capacity is in Fig. 1. The cap on lists "the first 400 microns of a total thickness of 2 mm". Was the thickness of the electrode really 2mm? Or is this the "lateral thickness"? If the later, how is C-rate defined? This was confusing.
The authors have made a deliberate choice to exclude the use of the term "C-rate" in reference to the op cal experiment, as previously explained in response to the aforemen oned comment. As a result, the term "effec ve-C-rate" has been completely eliminated from the manuscript. To provide further clarifica on, the total "thickness" refers to the width of the graphite strip, which measures 2.2 mm. This is based on the lithia on direc on of the electrode. In order to examine the relevant dynamics, a por on of the full width, specifically the first 400 um, was observed under a magnifica on of 700x. This chosen range is sufficiently large to effec vely demonstrate the influence of charging current density and electrolyte concentra on gradient on the spa al dynamics of lithia on, phase separa on, and pla ng/relaxa on.
To aid in be er understanding, the revised manuscript includes visual representa ons of the defini on of "thickness" in the form of the new Figure 1, the cap on of Figure 2 (previously Figure 1), and the surrounding contextual explana ons.
3) The paper discusses "global SOC" several mes, but this term is not clearly defined. Is this referring to the charge of the electrode rela ve to the theore cal capacity of the en re electrode? Please explain how this is used in the various configura ons (op cal vs. coin cell, etc.).
The Reviewer's is correct, that the global state of charge (SOC) is indeed defined as the charged capacity divided by the theore cal capacity of the electrode. This differs from the par cle SOC, which reflects the lithia on state of an individual par cle. This was described in the first paragraph under Results as "the percentage and decimal number of SOC represents the lithium content in the electrode and par cle, respec vely." The authors have taken the feedback into considera on and have revised the sentence to enhance clarity. The updated sentence now reads as follows: "The percentage and decimal number of SOC represent the lithium content in the en re electrode (i.e., global SOC) and in the par cle, respec vely." 4) Why was the plated Li in Fig. 1 so out of focus? And in which direc on (rela ve to the microscope and electrode configura on" is the Li pla ng occurring? Is it constrained to only grow towards the separator (as would be typical in a coin cell), or is it growing out towards the microscope objec ve? Please clarify this in the text.
The authors would like to provide an explana on regarding the poten al factors that may impact the sharpness and clarity of the plated lithium in the images. One possible influence is the forma on of gas bubbles around the plated lithium, which can affect its overall appearance. Another factor to consider is the shiny reflec on of Li, which can result in the loss of surface detail and affect the visual quality of the images. It is worth no ng that these issues are unlikely to be caused by focus-related problems, as all the images were captured using a depth-of-field composi on mode. This specific mode was employed to ensure the sharpness and clarity of the images, minimizing any poten al focus-related issues.
The growth of plated lithium occurs laterally, specifically at the lateral surface of the electrode (LSE), where it can expand freely without any constraints. Thanks to the Reviewer's comment, extra labels have been incorporated into Figure 2 to enhance the visual representa on and understanding of the lateral growth of plated lithium.
5) The text refers to the EEI as the "electrode electrolyte interface". Does this mean electrode-separator interface? This terminology is confusing, because there is electrolyte present throughout the porous electrode geometry. Also, is there any electrolyte on the top surface (towards the microscope objec ve) that is not within the pores of the electrode? If so, wouldn't there be concentra on gradients and electrolyte transport effects within this "top" region (perpendicular to the electrode-separator interface)? This was not clear, and again, might be more clearly shown when adding the cell geometry informa on to the main text.
The term "EEI" was originally used to refer to the interface between the lateral surface of the electrode and the bulk of the electrolyte. The authors acknowledge that this terminology can be confusing, as the term "EEI" is commonly used to denote the electrode/separator interface in coin cell or pouch cell designs. Therefore, the authors have made the necessary revision in the manuscript. The term "EEI" has been replaced with "LSE" (lateral surface of the electrode) throughout the revised manuscript to provide clarity and avoid any poten al confusion.
There is minimal or no presence of electrolyte between the electrode and the glass at the top due to the ghtly bonded contact between them. To ensure this in mate contact, any bubbles formed at the interface of the electrode and glass were carefully removed using a syringe during the electrolyte injec on into the cell. This procedure further guarantees the establishment of op mal contact. If there were electrolyte present on the top surface of the electrode, one would expect a homogeneous color change of the graphite par cles throughout the electrode instead of the observed phenomenon of ini a on from the lateral edges during the charging process. In the revised manuscript, the authors have included addi onal details in the first paragraph of the Results sec on, as follows "The top surface of the electrode strip is in close contact with the glass (Fig. 1a), where the electrolyte accessibility is limited, and the bo om of the strip is copper current collector, in contact with the separator. Thus, the Li + ions mainly intercalate from the lateral surfaces towards deeper region of the graphite electrode ( Fig. 1c and d)." 6) In the paragraph below figure 1, "nominal current density" is used for the first me. What is meant by this, and how does it relate to "effec ve C-rate" described above?
Nominal current density refers to the intended or expected charging current density to be applied in the experiment, which only lasted for 1 hour due to the occurrence of lithium pla ng. To prevent any poten al confusion, the authors have deleted the word 'nominal'. 7) Overall, the reviewer found the op cal microscopy sec on the most difficult to follow-in the paper. It was not clear how some of these terms were defined (C-rate, current density, etc." rela ve to the areal capacity fo the porous electrode rela ve to the current collector, vs. the direc on of lithia on. It should be emphasized to the reader if this visualiza on is actually in the in-plane (lateral direc on) of a "typical" electrode, and that the corresponding direc on of SoC gradients observed is perpendicular to what is normally considered the "thickness" direc on, which was unclear. That would help to clarify several of the points above.
In summary, the authors have made the following changes according to the Reviewer's sugges on: (1) A new Figure 1 has been introduced, featuring comprehensive labels, arrows, referen al axes, and a schema c representa on that illustrates the sample geometry, spa al arrangement, viewing angle, and lithia on direc on. Notably, the Li + inser on direc on and the thickness direc on have been emphasized with labels and arrows in mul ple panels.
(2) Addi onal descrip ons have been added in the first paragraph in Result sec on to provide further clarity and ensure a be er understanding of the aforemen oned aspects: "The top surface of the electrode strip is in close contact with the glass (Fig. 1a), where the electrolyte accessibility is limited, and the bo om of the strip is copper current collector, in contact with the separator. Thus, the Li + ions mainly intercalate from the lateral surfaces towards deeper region of the graphite electrode ( Fig. 1c and d), and accordingly the current density is calculated as the ra o of the total current and the four lateral surface areas of the rectangular graphite electrode. Note that the 'thickness' in the op cal experiment refers to the in-plane horizontal distance in lithia on direc on of the electrode strip (x-direc on, Fig. 1c), which is much larger than the conven onal thickness of the electrode coa ng (z-direc on, Fig. 1d)." 8) All of the experiments in this paper appear to be 2-electrode measurements with a Li metal counter electrode and no reference electrode. Therefore, in the experimental voltage curves, although the graphite poten al is plo ed as "vs Li/Li+", the effects of overpoten als at the Li metal counter electrode (which is not at 0V during non-zero currents) and IR drop will impact the measured poten al. It was not clear, therefore, how it could be determined that 20 mV is the energy barrier for nuclea on. This was also confusing, because it was not clear if the authors were sta ng that the electric poten al of the composite graphite anode (composed of many par cles at different SOC) is the nuclea on barrier, or if this barrier applies to the electrochemical poten al of individual graphite par cles, which are at different SOC. Please clarify how this single number is used in this defini on, and how it relates to inter-par cle SoC heterogeneity.
The authors acknowledge that the measured voltage may be subject to shi s caused by the overpoten al at the Li metal anode and IR drop. However, it is important to clarify that the determina on of the pla ng nuclea on barrier of 20 mV was not based on the voltage curve and was not influenced by the IR drop or overpoten al at the Li anode (i.e., not by fi ng the predic on with the experiment). The nuclea on barrier for Li pla ng is an intrinsic parameter of the material and is associated with the surface condi on, including factors such as defects, geometry, crystalline orienta on, and the electrolyte used.
Pla ng ini a on occurs at a localised point on the surface of individual graphite par cles, rather than occurring uniformly across the electrode. Hence, in this study, the nuclea on energy barrier for pla ng was specifically applied to each individual graphite par cle, rather than using a single overpoten al value for the en re composite electrode. The pla ng propensity varies from par cle to par cle, depending on their unique local electrochemical condi ons.
The determina on of the nuclea on energy barrier was carried out as follows: the pla ng kine cs (can be found in the SI and it is copied below) indicated that a nuclea on energy barrier (E b ) was incorporated into the calcula on of the local pla ng kine cs for each individual par cle. Following the ini a on of pla ng, this energy barrier exponen ally decreases as the pla ng thickness increases. This exponen al rela onship was established based on the findings presented in T. Gao et al.'s research published in Joule (5, 393-414) by Bazant and colleagues. E b , the nuclea on energy barrier, was determined by comparing the phase and SOC distribu on of Li intercalated in the electrode along the horizontal thickness direc on. This comparison was made between the experimental observa ons and predic ons (as shown in Figure S4 of the revised Supplementary Informa on) at the end of the charge and relaxa on processes. If E b is over-es mated, it results in an underes ma on of the plated lithium, which in turn leads to an overes ma on of the intercalated Li. This is indicated by a shi in the phase boundaries and SOC distribu on towards the right-hand side of the field-of-view. Consequently, during the relaxa on phase, the propaga on of the phase boundary (e.g., the gold/red boundary in Figure S4c and d) resul ng from the re-intercala on of the plated lithium is less pronounced due to the underes mated pla ng. Conversely, if E b is underes mated, the opposite effects occur. Through careful analysis, it was determined that an E b value of 20 mV provides the op mal consistency with the experimental results. However, it is worth no ng that the predicted relaxa on voltage curve exhibits a more extended stripping process compared to the experimental data (as shown by the green curve in Figure S3a). This discrepancy could poten ally be a ributed to the model's inability to account for the forma on of dead lithium during stripping, as it assumes all plated lithium is reversible. Nonetheless, the possible presence of dead Li does not influence our procedure to es mate the nuclea on barrier from the SOC distribu on and shi in phase boundary during charge.
9) The discussion of the individual par cle geometries, orienta ons, size effects etc. was great, and a true highlight of the paper. One thing that was not clear is the term "Li flow direc on". What is meant by that? Are the authors referring to the vector poin ng normal to the electrode/separator interface? Li is clearly "flowing" in 3-dimensions within this 3-d electrode geometry, so this terminology was not clear. How does this "flow direc on" relate to the electric field direc on in the electrolyte phase surrounding these individual par cles? It seems that the electrolyte poten al gradients will also lead to a 3-D distribu on of the electric field in the vicinity of the individual par cles, so it was not clear what the "flow direc on" indicates.
In the main text, the term "Li flow direc on" is used to indicate the overall lithia on direc on of the electrode. The authors acknowledge that this expression may not be precise, as it could poten ally be misconstrued as referring to the local movement of Li ions within the electrolyte. The trajectory of Li ions within the electrolyte is indeed intricate, influenced by factors such as electrolyte concentra on, Li ionic poten al, and par cle geometry.
To eliminate any confusion arising from this terminology, the authors have decided to subs tute "Li flow direc on" with the phrase "global lithia on direc on" 10) The authors state that "intra-par cle SOC heterogeneity cannot be captured by macroscopic modelling techniques and yet is the major cause of the early onset of lithium pla ng". What is meant by "the major cause"? Inter par cle heterogeneity (including SoC gradients throughout the electrode thickness) lead to local current focusing, which accelerates intra-par cle heterogeneity. So it seems that both intra-and inter-par cle SoC heterogeneity are coupled in a composite electrode, and we can not state that one is the "major cause" vs. the other.
The authors totally agree with the Reviewer's point of the inter-dependence of the inter-par cle and intrapar cle SOC heterogeneity. The uneven lithia on at the electrode scale can contribute to intra-par cle SOC heterogeneity, which can be influenced by various factors such as surface morphology, shape, and size of the par cles as well. Although the authors specifically men oned intra-par cle SOC to emphasize early pla ng at the par cle level due to the heterogeneous SOC distribu on, we agree that inter-par cle SOC heterogeneity is also significant and should not be overlooked. To address this concern, the authors have incorporated the following change in the revised manuscript: "However, intra and inter-par cle SOC heterogenei es cannot be captured by macroscopic modelling techniques and yet are the major causes of the early onset of lithium pla ng." 11) The 3-D microstructure characteriza on sec on provides details that do not seem to directly relate to the rest of the story of the paper. For example, it was not clear how the details in Fig. 3d-j directly relate to the discussion? Perhaps the most relevant point is the significant differences in tortuosity factor in the ver cal vs. horizontal direc ons. It is worth men oning that the op cal cell geometry will thus experience greater electrolyte transport limita ons than the coin cell, if the direc on of "thickness" is in the horizontal direc on.